Question: Simplify the following expression: $ n = \dfrac{1}{5} - \dfrac{k + 4}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{1}{5} \times \dfrac{7}{7} = \dfrac{7}{35} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{k + 4}{7} \times \dfrac{5}{5} = \dfrac{5k + 20}{35} $ Therefore $ n = \dfrac{7}{35} - \dfrac{5k + 20}{35} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{7 - (5k + 20) }{35} $ Distribute the negative sign: $n = \dfrac{7 - 5k - 20}{35}$ $n = \dfrac{-5k - 13}{35}$